Positive displacement rotary pumps, known as “lobe pumps,” are widely used in industries such as pulp and paper, chemical, equipment, food, beverage, pharmaceutical, and biotechnology. Lobe pumps can pump a wide variety of materials at continuous or intermittent flows.
A standard three-lobe pump is shown in FIGS. 1A-1C. Two identical rotors 10, 12 rotate in opposite directions around their respective axes of rotation 14, 16 to mesh as shown. The axes of rotation 14, 16 are separated by a distance l.
Each rotor has multiple lobes 20. The lobes of each of the rotors 10, 12 come in close proximity to the other rotor and to the interior of the lobe pump casing 30, so that material 40 can be trapped between the lobes 20 of the rotors 10, 12 and the pump casing 30.
As the rotors rotate within the lobe pump casing 30, material 40 flows into an inlet end 32 of the casing 30 (FIG. 1A), is subsequently trapped between the lobe 20 of a rotor 10 and the casing 30 (FIG. 1B), and then is pushed out of the pump through the outlet end 34 (FIG. 1C). As the lobes rotate, the material 40 travels around the outside of the rotors 10, 12.
The rotors of a standard lobe pump can be rotated by a driving gear 52 and a driven gear 50, as shown in FIG. 2A. As shown, the rotors 10′, 12′ can each have two lobes 20′ instead of the three shown in FIGS. 1A-1C, or rotors can alternatively be designed to have any number of lobes. The rotor frequency n is the same as the frequency of its driving motor, and is related to a pumping period T by the following expression:
      n    =          1              2        ⁢        NT              ,where N is the number of lobes on each rotor.
Profiles for the rotors within a lobe pump can be designed using the “deviation function method.” See, e.g., Yang, Tong, and Lin, “Deviation-Function Based Pitch Curve Modification for Conjugate Pair Design,” J. of Mech. Des. v. 121, pp. 579-586 (1999), the entire contents of which are incorporated herein by reference. This method uses a function that describes the deviation of the conjugate pair (or rotor pair) from the profile of a pitch pair, such as a pair of ellipses or circles rotating in opposite directions while maintaining contact. This method allows one skilled in the art to generate a profile of a conjugate pair with a desired geometry so that it matches the rotation of a given pitch pair. For example, the deviation function method could generate a rotor profile with a desired number of lobes of a desired length and noncircularity, etc., that rotates with another rotor similarly to a pair of oppositely rotating circles. This reference allows a broad range of rotor profiles to be generated that correspond to given pitch pairs, but suggests no particular geometry for the rotor or the effects of such geometry.
There are typically two types of lobe pumps used in the industry: conventional, involute lobe pumps and epitrochoidal lobe pumps. FIG. 3A shows a profile of a conventional involute lobe pump rotor. Involute lobe pump rotors have a smooth, continuous profile.
Epitrochoidal lobe pumps have rotors with profiles composed of circular arcs and epitrochoidal curves that do not have first order continuity at some intersections of curve segments. An example of lobe profiles of epitrochoidal rotors is shown in FIG. 4.
Resultant flow rates of conventional lobe pump systems or systems with rotor profiles generated through the deviation function method, described above, have also been previously described by Applicants in “The specific flowrate of deviation function based lobe pumps—derivation and analysis,” Mechanism and Machine Theory 37, pp. 1025-1042 (2002), the entire contents of which are incorporated herein by reference.
In this reference, a normalized flow rate can be derived from a given profile that deviates from an non-circular or circular pitch profile according to a given deviation function, e(θ). Specifically, a flow rate in terms of an angle of rotation θ of the rotor can be expressed as:
            F      ⁡              (        θ        )              =                                        θ            .                    ·                      l            ⁡                          (                                                b                  2                                -                                  r                  ⁡                                      (                                          l                      -                      r                                        )                                                  -                                                      e                    ⁡                                          (                      θ                      )                                                        2                                            )                                      ⁢        w                    2        ⁢                  (                      l            -            r                    )                      ,where, referring to FIGS. 2B-C, l represents the distance between the rotors' axes of rotation 140, 160, w is the rotor thickness, b is the lobe length, r is the distance from the axis of rotation 160 of the rotor 120 to a contact point P. The contact point P is the point of contact of the rotors' 140, 160 respective pitch profiles p1, p2. e(θ) is the deviation function, or a function showing the deviation of the profile of the actual rotor 120 from its corresponding pitch profile p1.
It is known that a flow rate of material out of a conventional, involute lobe pump will be a periodic, parabolic function of the angular position θ of the pump rotors, as shown in FIG. 3B. See, Mimmi, 1992; Mimmi and Pennacchi, 1994. The amplitude variation of the periodic function is due to the change of the contact point position of the rotors during the meshing. These periodic functions are described in more detail in, e.g., Yang and Tong, 2000; Bidhendi et al., 1983; and Iyoi and Togashi, 1963. It is also known that the flow rate of material out of epitrochoidal lobe pumps is constant. See Mimmi and Pennacchi, 1994.
One problem present with both existing conventional lobe pump systems is that a user is limited to either a specific constant or a specific periodic parabola flow rate, depending on the type of conventional rotor the user chooses. If a particular periodic flow rate is required for an application, such as a volume of flow that varies sinusoidally with time or angle of rotation, neither of the conventional lobe pump types would be sufficient. Further, even if a periodic parabola or constant type flow rate is required, a user is currently limited to a small number of standard lobe profiles from which to choose. Thus, a user would likely need to employ an entirely different, and costlier, type of pump to achieve a desired flow rate.